Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
bool check(long long n) {
  n *= 2;
  long long sq = sqrt(n);
  return (sq * (sq + 1) == n);
}
int main(int argc, char** argv) {
  long long n;
  cin >> n;
  vector<int> v;
  int z = 0;
  for (long long i = 1; i * (i + 1) / 2 < n; i++) {
    long long x = i * (i + 1) / 2;
    if (check(n - x)) {
      cout << "YES" << endl;
      z = 1;
      break;
    }
  }
  if (z == 0) cout << "NO\n";
  return 0;
}